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Properties

Label 264.48.1.zz.1
Level $264$
Index $48$
Genus $1$
Cusps $8$
$\Q$-cusps $4$

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Invariants

Level: $264$ $\SL_2$-level: $24$ Newform level: $1$
Index: $48$ $\PSL_2$-index:$48$
Genus: $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (of which $4$ are rational) Cusp widths $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ Cusp orbits $1^{4}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24G1

Level structure

$\GL_2(\Z/264\Z)$-generators: $\begin{bmatrix}1&188\\256&57\end{bmatrix}$, $\begin{bmatrix}27&104\\130&77\end{bmatrix}$, $\begin{bmatrix}58&65\\145&246\end{bmatrix}$, $\begin{bmatrix}97&132\\12&181\end{bmatrix}$, $\begin{bmatrix}121&150\\244&143\end{bmatrix}$, $\begin{bmatrix}133&182\\82&105\end{bmatrix}$, $\begin{bmatrix}145&228\\90&211\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 264.96.1-264.zz.1.1, 264.96.1-264.zz.1.2, 264.96.1-264.zz.1.3, 264.96.1-264.zz.1.4, 264.96.1-264.zz.1.5, 264.96.1-264.zz.1.6, 264.96.1-264.zz.1.7, 264.96.1-264.zz.1.8, 264.96.1-264.zz.1.9, 264.96.1-264.zz.1.10, 264.96.1-264.zz.1.11, 264.96.1-264.zz.1.12, 264.96.1-264.zz.1.13, 264.96.1-264.zz.1.14, 264.96.1-264.zz.1.15, 264.96.1-264.zz.1.16, 264.96.1-264.zz.1.17, 264.96.1-264.zz.1.18, 264.96.1-264.zz.1.19, 264.96.1-264.zz.1.20, 264.96.1-264.zz.1.21, 264.96.1-264.zz.1.22, 264.96.1-264.zz.1.23, 264.96.1-264.zz.1.24, 264.96.1-264.zz.1.25, 264.96.1-264.zz.1.26, 264.96.1-264.zz.1.27, 264.96.1-264.zz.1.28, 264.96.1-264.zz.1.29, 264.96.1-264.zz.1.30, 264.96.1-264.zz.1.31, 264.96.1-264.zz.1.32, 264.96.1-264.zz.1.33, 264.96.1-264.zz.1.34, 264.96.1-264.zz.1.35, 264.96.1-264.zz.1.36, 264.96.1-264.zz.1.37, 264.96.1-264.zz.1.38, 264.96.1-264.zz.1.39, 264.96.1-264.zz.1.40, 264.96.1-264.zz.1.41, 264.96.1-264.zz.1.42, 264.96.1-264.zz.1.43, 264.96.1-264.zz.1.44, 264.96.1-264.zz.1.45, 264.96.1-264.zz.1.46, 264.96.1-264.zz.1.47, 264.96.1-264.zz.1.48, 264.96.1-264.zz.1.49, 264.96.1-264.zz.1.50, 264.96.1-264.zz.1.51, 264.96.1-264.zz.1.52, 264.96.1-264.zz.1.53, 264.96.1-264.zz.1.54, 264.96.1-264.zz.1.55, 264.96.1-264.zz.1.56, 264.96.1-264.zz.1.57, 264.96.1-264.zz.1.58, 264.96.1-264.zz.1.59, 264.96.1-264.zz.1.60, 264.96.1-264.zz.1.61, 264.96.1-264.zz.1.62, 264.96.1-264.zz.1.63, 264.96.1-264.zz.1.64
Cyclic 264-isogeny field degree: $24$
Cyclic 264-torsion field degree: $1920$
Full 264-torsion field degree: $20275200$

Jacobian

Conductor: $?$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: not computed

Rational points

This modular curve is an elliptic curve, but the rank has not been computed

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_0(3)$ $3$ $12$ $12$ $0$ $0$ full Jacobian
88.12.0.bb.1 $88$ $4$ $4$ $0$ $?$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_0(12)$ $12$ $2$ $2$ $0$ $0$ full Jacobian
88.12.0.bb.1 $88$ $4$ $4$ $0$ $?$ full Jacobian

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
264.96.1.rm.1 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rm.2 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rm.3 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.rm.4 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.ro.1 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.ro.2 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.ro.3 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.ro.4 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sw.1 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sw.2 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sw.3 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sw.4 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sy.1 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sy.2 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sy.3 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.1.sy.4 $264$ $2$ $2$ $1$ $?$ dimension zero
264.96.3.fe.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.fx.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.iv.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.iw.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.jt.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.jv.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.kf.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.kh.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.lo.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.lr.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.mr.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.ms.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.ng.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.nj.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.nt.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.nu.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qh.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qh.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qh.3 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qh.4 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qj.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qj.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qj.3 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.qj.4 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rf.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rf.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rf.3 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rf.4 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rh.1 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rh.2 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rh.3 $264$ $2$ $2$ $3$ $?$ not computed
264.96.3.rh.4 $264$ $2$ $2$ $3$ $?$ not computed
264.144.5.pp.1 $264$ $3$ $3$ $5$ $?$ not computed